The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 36 mg of Sr-90, how many milligrams will remain after 152.4 years?

Question

The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 36 mg of Sr-90, how many milligrams will remain after 152.4 years?

Answer 1

The decay equation is N = N₀ e^-λt. After 38.1 years, N = N₀ / 2, so N₀ / 2 = N₀ e ^{-λ x 38.1} .

Take the ln of both sides, ln 0.5 = -λ x 38.1. Solve for λ to get λ = 0.0182,

Knowing λ, we can now find N = 36 e^{-0.0182 x 152.4} = 2.24 mg

please check calculations.